Bipartite density of cubic graphs

Authors:
Abraham Berman;Xiao-Dong Zhang
Affiliations:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel;Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, People's Republic of China and Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
Venue:
Discrete Mathematics
Year:
2003

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Abstract

We first obtain the exact value for bipartite density of a cubic line graph on n vertices. Then we give an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of the adjacency matrix. In addition, we characterize, except in the case n = 20, those graphs for which the upper bound is obtained.